Merits and Limitations of Standard Deviation

Merits:

(i)    The standard deviation is the best measure of variation because of its mathematical characteristics. It is based on every item of the distribution. Also it is amenable to algebraic treatment and is less affected by fluctuations of sampling than most other measures of dispersion.

(ii)    It is possible to calculate the combined standard deviation of two or more groups. This is not possible with any other measure.

(iii)    For comparing the variability of two or more distribution coefficient of variation is considered to be most appropriate and this is based on mean standard deviation.

(iv)    Standard deviation is most prominently used in further statistical work. For example, in computing skewness, correlation, etc., use is made of standard deviation. It is keynote in sampling and provides a unit of measurement for the normal distribution.

Limitations:

(i)    As compared to other measures it is difficult to compute. However, it does not reduce the importance of this measure because of high degree of accuracy of results it gives.

(ii)    It gives more weight to extreme items and less to those which are near the mean. It is because of the fact that the squares of the deviations which are big in size would be proportionately greater than the squares of those deviations which are comparatively small. The deviations 2 and 8 are in the ratio of 1:4 but their squares, i.e., 4 and 64 would be in the ratio of 1:16.

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